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Copyright 1991 by the American Psychological Association. Inc. 0033-2909/91/S3.00

Psychological Bulletin 1991, Vol. 109, No. 3, 490-501

Developmental Change in Speed of Processing During Childhood and Adolescence Robert Kail

Department of Psychological Sciences Purdue University Throughout childhood and adolescence, there are consistent age differences in speed of processing. Here 72 published studies yielded 1,826 pairs of response times (RTs) in which each pair consisted of adults' mean RT for a condition and the corresponding mean RT for a younger group. The primary results were that (a) children's and adolescents' RTs increase linearly as a function of adult RTs in corresponding conditions and (b) the amount of increase becomes smaller with age in a manner that is well described by an exponential function. These results are consistent with the view that age differences in processing speed reflect some general (i.e., nontask specific) component that changes rapidly during childhood and more slowly during adolescence. Possible candidates for the general component are discussed.

attributed to some single, global factor. They proposed that a general slowing of the nervous system would explain why the elderly respond more slowly than young adults on virtually all speeded tasks. Furthermore, this proposal led to a straightforward quantitative test. Suppose that young adults' response on a particular task consists of several processes, such that their RT is defined as

Age differences in performance on speeded tasks are large and remarkably consistent. In 1935, for example, Goodenough reported mean response times (RTs) to an auditory stimulus of 318 ms for 5- to 7-year-olds compared with 172 ms for adults. Children's responses were 1.85 times slower than adults. Thirtyfive years later, Elliot (1970) tested subjects on a similar task and reported means of 275 and 145 ms for 5- to 7-year-olds and adults, respectively. Here children were 1.9 times slower than adults. These and other studies of age differences in speeded performance were last reviewed by Wickens (1974), who tentatively concluded that "some irreducible maturational differences in processing rate are present" (p. 739). The aim of the work described here was to provide a precise, quantitative characterization of these age differences in an effort to identify the underlying mechanisms. I begin by introducing a hypothesis and associated methodology from the study of cognitive aging. These procedures are then applied to data from studies of children's and adolescents' speeded performance. Finally, I discuss mechanisms that might be responsible for age differences in speed of processing.

where a is the time to execute process A, b is the time for process B, and so on. If older adults execute each process more slowly, by a constant factor, then the corresponding equation for older adults would be

RT = ma + mb + me • • • = m(a + b + c),

(2)

where m is simply the slowing coefficient. Another possibility is that the magnitude of age differences varies across specific processes. That is, multiple slowing coefficients are proposed, which means that the hypothetical equation for older adults would be

RT = maa + mhb + mcc + •

A Multiplicative Model of Cognitive Slowing During Adulthood

(3)

where, for example, maa denotes the extent to which elderly adults are slower than young adults for process A. These views can be distinguished in experiments in which the number of processes is varied or manipulations are included that affect the duration of these processes. The result is a range of RTs for both young and old adults. According to the hypothesis of general slowing (i.e., a single slowing coefficient), the correlation across these conditions between young and older adults' RTs should be 1, because this is simply a correlation between a variable and that same variable multiplied by a constant. Two additional predictions concern the function in which older adults' RTs are expressed as a function of younger adults' RTs from the corresponding experimental conditions. The slope of this function should be greater than 1 and provides an estimate of m. The intercept should be 0, reflecting the fact

Like young children, elderly adults usually respond substantially slower than young adults. Initially, Birren (1965) and, later, Salthouse and Somberg (1982) and Cerella (1985) suggested that these age differences in response speed could be The work described here was supported by the National Institute of Child Health and Human Development Grant 19447.1 am grateful to Laura Curry and Ric Waits for their help in finding and analyzing these data. I thank Jeff Bisanz and Howard Zelaznik for their helpful comments on a previous draft. Correspondence concerning this article should be addressed to Robert Kail, Department of Psychological Sciences, Purdue University, West Lafayette, Indiana 47907.

490

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SPEED OF PROCESSING that, for both old and young adults, RT = 0 if no operations are performed. Thus, this explanation, hereafter called the multiplicative model, is simply expressed as

Y= mX,

(4)

where A'and Yare young and old RTs, respectively, and m is the slowing coefficient. Predictions from Equation 3 depend on specific values of ma, mb, and so on and on the number and times of specific processes A, B, and so on. For example, the specific correlation between young and old adults' RTs is small when ma and mb differ by orders of magnitude, but it increases as ma and mb converge, with an expected r of 1 in the degenerate case where ma = mb. The slope of the function relating old adults' RTs to young adults' RTs should be greater than 1, because this is a weighted average of the ma, mb, However, the slope should vary across different experiments, reflecting different combinations of ma and mb specific to the processes required in a particular task. Thus, the process-specific nature of this hypothesis makes it difficult to derive exact predictions from Equation 3. Nevertheless, it is evident that rs near 1 and slopes that are stable across tasks would be consistent with the multiplicative model; smaller correlations and variability in estimates of slopes across tasks would be consistent with the multifactor view of slowing. In fact, considerable evidence is consistent with the multiplicative model. Results reported by Salthouse and Somberg (1982) are typical. Subjects—20- and 71-year-olds—were tested on a memory-search task in which they studied a subspan set of digits and then decided if a single digit was a member of the set studied previously. The experiment involved eight conditions created by manipulating stimulus clarity, the number of digits studied, and response complexity. Consistent with the multiplicative model, the correlation computed across the eight conditions between younger and older adults' RTs was .991. Also consistent with the multiplicative model, the slope was greater than 1 and the intercept approximated 0. Furthermore, when data are pooled across experiments in which different tasks were used, a single slowing coefficient provides an adequate characterization of change in older adults' RTs as a function of younger adults' RTs (Cerella, 1985). More recent work in the area of cognitive aging has addressed the possibility that the relation between younger and older adults' RTs might be better described by power functions than by linear functions (Hale, Myerson, & Wagstaff, 1987) as well as the possibility of separate slowing coefficients for perceptualmotor and cognitive tasks (Cerella, 1985; cf. Salthouse, 1988). These issues are far from resolved (see Cerella, 1990), but do not bear directly on the present problem, which is simply to determine if child-adult differences in speeded performance are as systematic as the young adult-old adult differences. That is, can the same lawful relation be established between children's and adults' RTs that has been established for younger and older adults' RTs and that implies a general factor in adult age differences in speeded performance?

Tests of the Multiplicative Model During Childhood and Adolescence Children's responses on speeded tasks are typically much slower than those of young adults (Wickens, 1974). These age

491

differences in processing speed during childhood, adolescence, and young adulthood could be due to some general developmental factor, analogous to the common slowing coefficient implicated in studies of cognitive aging. That is, the factor would not be specific to particular tasks and would change systematically with age. For example, in information-processing theories, resources or attention are often required for performance on speeded tasks (Shiffrin & Dumais, 1981), and increasing resources typically increases processing speed (Anderson, 1983). Hence, an age-related increase in the amount of processing resources (e.g., Case, 1985) could produce age-related increases in processing speed. Furthermore, this age-related increase in resources would manifest itself in faster performance on all speeded tasks. To determine if a general factor is responsible for age-related change in processing speed, RTs from children and adolescents (hereafter referred to collectively as youths) as well as young adults' RTs can be fitted to Equation 4. Y now denotes youths' RTs, and m refers to the factor by which youths are slower than adults. Of course, the extent of slowing may depend on the age of the youths, a topic considered later. Consequently, Y, and mt are used to denote RTs and slowing coefficients, respectively, at a particular age /'. There are two studies in the child-development literature in which Equation 4 has been fitted to data from children, adolescents, and young adults. Kail (1986b, Exp. 3) tested 8-year-olds and adults on a mental rotation task in which they judged whether pairs of letters presented in different orientations were identical or mirror images. There were 24 conditions reflecting orthogonal combination of six orientations, two responses, and two degrees of stimulus degradation. The correlation, across the 24 conditions, between children's and adults' RTs was .93 with a slope (i.e., ms) of 1.66. Hale (1990) evaluated the relation between youths' and young adults' RTs with a wider range of speeded tasks and with multiple age groups. She tested 10-, 12- and 15-year-olds and adults on four speeded tasks: two-alternative choice RT, letter matching, mental rotation, and a task involving matching abstract patterns. At each age, eight mean response times were derived and correlated with adults' times for those conditions. The correlations between youth and adult RTs were greater than .99 at all ages. Values of m, were 1.82,1.56, and 1.00 for 10-, 12-, and 15-year-olds, respectively, indicating a gradual approximation to adults' processing time. In the studies by Kail (1986b, Exp. 3) and Hale (1990), the results were consistent with the claim that some general factor is responsible for age differences in processing time. To provide a more robust test of this claim, I completed an exhaustive search for studies of speeded performance published in three primary empirical journals of child-developmental psychology: Child Development, Developmental Psychology, and Journal of Experimental Child Psychology. Child Development was searched from 1960 through 1989. Developmental Psychology and Journal of Experimental Child Psychology were searched from their initial volumes (in 1969 and 1964, respectively) through 1989. Several criteria were used to select studies. First, a study had to include a sample of young adults and a sample of youths. Second, RTs had to be reported, and these had to be collected

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492

ROBERT KAIL

under instructions that, explicitly or implicitly, encouraged subjects to respond rapidly. Third, a study had to report mean RTs for at least six conditions. This requirement was imposed for purely practical reasons. Initial search made it clear that this criterion would provide sufficient data to perform the analyses of interest and would eliminate the need to record numerous studies in which only a single RT was reported. The search yielded 76 experiments that met these criteria. Deleted from the sample, for reasons described later, were four experiments by the current author (Kail, 1986b, Exp. 1 and 2; 1988, Exp. 1 and 2). This left the 72 studies (from 56 articles) listed in Table 1 for analysis, with a total of 1,826 pairs of youthadult mean RTs. That is, each case in the data consisted of a mean RT for young adults from one of the 1,826 conditions represented in Table 1, along with the mean time for youths for that same condition. These data were divided into 11 sets based on the age of the youths: 3- and 4-, 5-, 6- 7- 8-, 9-10-, 11 -, 12-, 13-, and 14-year-olds. Each of the 11 data sets was fitted to Equation 4. The fits, shown in Figure 1 and described in Table 2, were uniformly excellent, with R2s > .90. Values for mt were greater than 1 and, as Hale (1990) reported, tended to be smaller for adolescents than for children. Stated another way, m, seemed to decline nonlinearly as a function of age, approaching an asymptotic value of 1. Direct comparison of w, values at different ages is potentially problematic because of substantial differences among the data sets in the range of adult RTs included. To illustrate, in the data for 3- to 5-, 9- and 13-year-olds, all adult mean RTs were less than 4 s. In contrast, in the data sets for 6-, 8-, and 11-year-olds, some adult mean RTs were greater than 25 s. Of course, these differing ranges of adult RTs simply reflect the selection of particular tasks by the individual investigators listed in Table 1. However, it seemed desirable to estimate w f over comparable domains of X. Consequently, for the 11 data sets, all pairs in which the adult mean RT was greater than 2 s were deleted. These reduced data sets included 1,519 pairs of youth-adult mean RTs, or 83% of the original pairs. Some of the 11 data sets remained the same size. The largest absolute change was for 8-year-olds, for whom 105 pairs were deleted; the largest proportional change occurred for 14-year-olds, where the reduced set contained 64.7% of the original pairs. The reduced data sets were also fitted to Equation 4. The results are shown in the last three columns of Table 2. In every instance, Equation 4 accounted for substantial portions of variance in youths' mean RTs, with R2s 2: .813. Estimates of w, were similar to those based on all RTs and declined in a reasonably systematic manner with age. The results presented thus far provide considerable support for the hypothesis that youths respond more slowly than adults by a constant factor. Youth and adult RTs are consistently related and in a manner that is well described by a linear function with a slope greater than 1 and an intercept of 0. In addition, Table 2 includes one noteworthy result not anticipated from the multiplicative model represented by Equation 4: mi changed substantially and systematically with age. The youngest children (3- to 5-year-olds) had m, values that approximated 3, whereas the mean mi for 12- to 14-year-olds was 1.25. Furthermore, values for mt did not seem to change linearly with age.

Instead they change substantially in early and middle childhood and more slowly thereafter. An obvious next step toward understanding developmental change in processing speed would be a precise characterization of age-related change in m,. Nonlinear changes in age like those shown in Table 2 are often well described by exponential functions. For example, in the studies mentioned previously that were deleted from the present analyses (Kail, 1986b, 1988), the speeds of a number of specific mental processes changed exponentially with age. To illustrate, in Kail (1986b, Exp. 1) subjects were tested on a name-retrieval task used by Bisanz, Danner, and Resnick (1979) in which they judged physical and name similarity of pictures as well as the mental rotation task described earlier. Subjects were tested from 12 different age groups (8 to 21 years inclusive), thereby providing ample data to determine the shape of developmental functions. For both name retrieval and rate of mental rotation, developmental change was well described by an exponential function of the form

Y=a + be~

(5)

where a represents asymptotic processing time, e is the base of natural logarithms, a + b is the intercept (for x = 0, e~" = 1), c is a "decay" parameter that indicates how rapidly the function approaches a, and / is age. A simplified version of Equation 5 was used here to provide a precise characterization of change in mt as a function of age. Specifically, the predicted coefficient at maturity is 1, so Equation 5 becomes

m,•= \ + be~

(6)

where b, e, c, and /' are defined as before. Values of m, for the full and reduced data sets (from Table 2) were fitted to Equation 6 with STEPIT, a FORTRAN subroutine that yields least squares estimates of parameters. Equation 6 accounted for 76.92% of the variance in the slowing coefficients derived from the full set and 84.1% of the variance in the coefficients from the reduced data set. Estimates of b and c were 5.16 and .20811, respectively, for the full set and 5.1 and .20661, respectively, for the reduced set. The fit of the slowing coefficients from Table 2 to Equation 6 is shown in Figure 2. The full and reduced data sets were also fitted to hyperbolic and power functions that have been used previously to characterize nonlinear change (Kail, 1986a; Newell & Rosenbloom, 1981). The power function was of the form m,• = 1 + b(i + c)~d,

(7)

where 1 denotes the asymptotic value, /' is age, and the term b(i + d)~d provides the rate of approach to asymptotic value. For the hyperbolic function, d of Equation 7 was set to 1. These functions accounted for almost exactly the same amounts of variance in the two data sets. The hyperbolic accounted for 75.34% and 86.19% of the variance in mt values; comparable figures for the power function were 75.35% and 86.19%. The similarity reflects the fact that the estimated value of d for the power function (i.e., Equation 7) was 1, which meant that the best fitting power function was actually hyperbolic.

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SPEED OF PROCESSING

These functions account for approximately the same amounts of variance as the exponential (i.e., Equation 6). However, the hyperbolic and power functions are problematic because the estimated values of c were negative (e.g., —2.07 for the fit of the hyperbolic to the full data set), which produces discontinuous developmental functions. Increasingly negative values of mt are predicted between 0 and |c| years, and mi is undefined at age |c|. For this reason, the remaining analyses focus exclusively on the exponential, which yields a continuous developmental function. To summarize, the analyses presented thus far lead to two conclusions. First, across a wide range of conditions, youths' RTs can be expressed as a multiple of adults' RT for that condition, indicating that some general factor is involved in age-related change in speeded performance. Second, speeded performance changes nonlinearly with age in a manner that is well described by an exponential function. In the remainder of this section, I provide additional evidence to support these conclusions. In both cases, the evidence involves evaluating the fit of extant data sets to values of w, derived from Equation 6. Studies of Developmental Functions Recall that I deleted from analysis studies in which developmental functions were estimated for different cognitive processes (Kail, 1986b, 1988). Each of these studies can be used to evaluate Equations 4 and 6 as a characterization of age-related change in processing time. To illustrate, consider the Kail (1986b, Exp. 1) study in which 8- to 21 -year-olds were tested on two tasks: mental rotation and name retrieval. At each age there were 12 mean RTs, 6 per task, that were fitted to Equation 4. (For these analyses, the data from 18- to 21-year-olds were pooled to form an adult group.) Equation 4 accounted for no less than 99.65% of the variance in youths' RTs. Furthermore, w, values declined nonlinearly, as shown in the top left panel of Figure 3. Also shown in Figure 3 is the exponential function derived from Equation 6 with b = 5.16 and c = .20811. The fit is quite good; Equation 6 accounts for 98.13% of the variance in the observed slowing coefficients. It is important to emphasize that the function in Figure 3 was not derived empirically from the data in that figure. Instead it was determined independently, with the values for b and c that were estimated from the slowing coefficients in Figure 2 and Table 2. This same analysis was performed on the data from the two experiments in Kail (1988). In Experiment 1,8- to 21-year-olds were tested on visual-search and memory-search tasks. At each age there were 12 mean RTs that resulted from orthogonal combination of two tasks, three set sizes (search sets for visual search, study sets for memory search), and two responses (yes, no). The mean RTs for 8- to 17-year-olds were fitted to Equation 4; the mean RTs for 18- to 21-year-olds constituted the adult data. Equation 4 accounted for no less than 99.54% of the variance in youths' RTs. As shown in the bottom left panel of Figure 3, values of mt declined with age. The exact rate of change is predicted quite well by Equation 6, with b = 5.16 and c = .20811: 93.96% of the variance was accounted for. Note again that this is parameter-free prediction inasmuch as the exponential function in Figure 3 is derived from the data in Figure 2. Experiment 2 in Kail (1988) included four tasks: mental rota-

493

tion, memory search, mental addition, and analogical reasoning. At each age, 24 mean RTs were calculated, 6 for each task. For mental rotation, a mean RT was calculated at each of 6 orientations. For memory search, a mean RT was calculated for each of three search set sizes (1, 3, 5), separately for yes and no responses. The mental-addition task included problems of the form w + y= z, with w and y ranging from 1 to 9. All possible combinations of w and y were included except "tie" problems (e.g., 1 +1, 3 4- 3), which resulted in 72 problems. Each was presented twice, once with the correct sum and once with an incorrect sum. For the present analyses, mean RTs were calculated for 24 small (3-8), 24 medium (9-11), and 24 large (12-17) sums, separately for true and false answers. The analogical reasoning task was one used by Stone and Day (1981), who modeled it after Raven's Progressive Matrices. Each problem consisted of three rows, and each row consisted of three squares that contained different geometric figures. Moving from left to right in each row, the figures were transformed (e.g., increased in size or increased in number). The subjects' task was to identify the changes present in the first two rows and then determine if these changes were present in the third row. Mean RTs were calculated for problems with zero, one, or two transformations, separately for problems in which the last row included the same transformations and for problems that did not. The 24 mean RTs at each of ages 8 to 17 years were fitted to Equation 4; the mean RTs for 18- to 21-year-olds made up the adult group. Equation 4 accounted for no less than 89.1% of the variance in the youths' RTs. The values for mh shown in the top right panel of Figure 3, are systematically smaller than those predicted from Equation 4, which accounts for 81.8% of the variance in observed mt values. The source of this discrepancy lies in the analogical reasoning task. The original analyses yielded several interactions with age that suggested qualitative change in performance with age. I return to this general point later. For now, it is sufficient to say that age differences on the reasoning task were smaller than expected. This, coupled with the fact that RTs on this task were substantially larger than those on the other tasks, with means typically greater than 5 s, produced shallower slopes (i.e., smaller values of mt) than would be expected. Consequently, I refitted Equation 4 to the data from Kail (1988, Exp. 2) but deleted the data from the analogical reasoning task. Equation 4 accounted for no less than 97.68% of the variance in youths' RTs. Values of w,, shown in the bottom right panel of Figure 3, declined systematically with age. Equation 6 accounted for 97.32% of the variance in these mt values. Thus, analysis of these data, like the analyses of the other data sets depicted in Figure 3, yielded two key results: (a) At each age, youth-adult RTs are highly related, and (b) m,, the slope of the function that relates increases in youth RTs to increases in adult RTs, changes exponentially with age. Impact of Practice With practice, adults and children execute cognitive processes more rapidly. For example, after extensive practice, (text continues on page 496)

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ROBERT KAIL

Table 1 Studies Included in the Analysis Youths' ages (yr)

Study Akhtar & Enns (1989, Exp. 1) Barrett & Shepp ( 1988) Bisanz, Danner, & Resnick(1979) Bisanz &Resnick( 1978) Chi &Klahr( 1975) Childs&Polich(1979) Duncan &Kellas( 1978) Elliot (1970) Emmerich & Ackerman (1979) Enns (1987) Exp. 1

Source of Data

Classification

9

Figure 2

7.67, 10.58 8.5, 10.42, 12.67

Classification Picture & name matching

8 6

Tables 1 and 2 Table 2

8.58, 10.5, 12.67 5.67 9.25, 11.08 8.3, 10.7, 12.3 6,9, 12" 7,9

Visual search Quantification Mental rotation Picture & name matching Simple RT Judgments of acoustic & semantic features

18 8 14 12 60 16

6,8.4,9.11

4.3, 5.5, 7.4 6.4, 8.3 4.6, 7.1

Same-different judgments Same-different judgments Same-different judgments Classification Classification Classification

7.6, 9.8 5.2, 7.8 6.1,8.4, 11.1

Classification Classification Classification

5

Matching-to-sample

6

Table 3

8.75,9.5, 11,5 8.42, 9.75, 12 7, 8, 10

Reading Visual search Same-different judgments

9 9 8

Figure 1 Figure 2 Figure 3

9a 9" 8, 11" 10.3, 13.5, 16.6 7,9"

Classification Classification Visual search Temporal judgments Visual search

6 12 24 14 8

Figure 3 Figure 4 Table 2 Figures 1, 3 Table 1

8.83, 10.83 8.58, 10.92 4.8, 7.7 6.4, 6.8, 9.6, 9.9

Visual search Visual search Simple RT Stroop task

12 7 10 6

Figure 2 Figure 3 Tables 1,3 Figure 2

6.9,8.1,9, 10.8 5.42, 8.83

Judgments of category membership Picture & name matching

5.7, 8, 10 5.7, 8, 10

6,8.4,9.11

Exp. 3

8, 10

Foreman (1967) Exp. 1 Exp. 1 Exp. 2 Friedman (1986, Exp. 3) Friedrich, Schadler, & Juola(1979) Gitomer, Pellegrino, & Bisanz (1983) Exp. 1 Exp. 2 Guttentag(1985) Guttentag & Haith (1978) Horn & Manis (1987, Exp. 1) Hoving, Morin, & Konick(1974) Juola, Schadler, Chabot, & McCaughey(1978) Kail (1985) Kail(1986a) Kail(1986b, Exjx 3) Kail, Pellegrino, & Carter (1980) Exp. 1 Exp. 2

Number of conditions

4.9,7,9.1

Exp. 2

Enns & Akhtar (1989) Enns &Brodeur( 1989) Enns & Cameron (1987) Enns &Girgus( 1985) Exp. 1 Exp. 2 Enns &Girgus(1986, Exp. 2) Farnham-Diggory & Gregg (1975) Fisher & Lefton ( 1976) Exp. 1 Exp. 2 Exp. 3

Task

Figure 2 Figure 1 Figure 2 Figures 1-3 Figures 1, 2 Table 2

6

Table 1

12

Table 2

12

Table 3

7

10 8

Table 1 Table 2 Table 1

10 10 8

Figure 2 Figure 6 Figures 4, 5

6

Table 4

6

Table 1

Visual search Visual search

6 12

Figure 1 Table 5

11, 14.33 9.5, 13.3 10.2

Mental rotation Mental rotation Mental rotation

18 6 24

Figure 3 Figure 2 Figure 4

9.17 8.5, 11.5

Mental rotation Mental rotation

12 12

Figure 1 Figure 1

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SPEED OF PROCESSING

495

Table 1 (continued) Youths' ages (yr)

Study Kerr, Blanchard, & Miller Exp. 1 Exp.2 Kerr, Davidson, Nelson & Haley (1982) Lefton& Fisher (1976) Exp. 3 Exp. 5 List, Keating, & Merriman (1985) Lorch, Lorch, Gretter, & Horn (1987) Manis, Keating, & Morrison (1980) Mansfield (1977, Exp. 2) McCaughey, Juola, Schader, & Ward (1980) Merriman, Keating, & List (1985) Morin, Hoving, & Konick(1970) Morrison (1982, Exp. 1) Nelson & Kosslyn (1975) Posnansky & Raynor (1977) Exp. 1 Exp. 3 Raynor (1986) Rosinski, Golinkoff, & Kukish( 1975, Exp. 1) Schwantes(1985) Exp. 1 Exp.2 Schwantes, Boesl, & Ritz( 1980, Exp. 1) Sekuler & Mierkiewicz (1977) Simpson & Lorsbach (1983) Exp. 1 Exp.2 Stanovich, West, & Pollak(1978) Sternberg & Rifkin (1979) Exp. 1 Exp.2 Stone & Day (1981) Tomlinson-Keasey, Kelly, & Burton (1978) Townsend & Ravelo (1980) Well, Lorch, & Anderson (1980, Exp. 2) West & Stanovich (1978)

Task

7.67,9.67, 11.58 7.75 8.4, 10.4, 12.4, 14.4

Choice RT Choice RT Choice RT

8.92, 10.08 8.83 9.8, 14.1

Visual search Visual search Picture & name matching

10.16, 12.1

Reading

7.92, 11.83

Number of conditions

Source of Data

9 6 9

Figure 1 Figure 3 Table 2

36 32 6

Figure 2 Figure 3 Table 2

8

Table 1

Picture & name matching

12

Table 2

5.33,7,9, 11.08 7.33

Recognition memory Visual search

8 18

Table 3 Table 1

9.67, 13.92

Mental rotation

7

Figure 2

6.33, 10.33

Judgments of category membership Same-different judgments Judging sentence truth

16

6.58,8.42, 11.42 6.58,8.25, 11.67 7.58,9.33, 11.42 7.58, 11.33

Stroop task Stroop task Reading Stroop task

6 8 14 6

8.5 9.08 8.83, 11.83

Reading Reading Reading

8 8 8

Table 3 Table 4 Figure 1

5.89, 6.88, 10.18, 13.13

Judgments of inequality

8

Figure 1

8.33, 10.17, 12.08 8.33, 10.08, 12.08 8.67, 11.58

Same-different judgments Reading

15

Table 1

6

Table 2

9

Table 1

8, 10, 12° 8, 10, 12' 10.92, 14.08 8.67, 13.25

Analogies Analogies Analogies Same-different judgments

12 6 18 8

Figure 3 Figure 4 Table 1 Table 3

3.58,4.58,5.25

10

Table 1

6.92

Picture-sentence matching Classification

6

Table 2

9.75, 11.5

Reading

8

Figures 1-3

5.6, 8.4

7.92, 10.92, 12.92

Visual search

Note. RT = response time. ' Ages not reported but estimated according to the formula age = grade + 5.5.

Figures 1, 2

8

Figure 1

6

Tables 2, 3

Table 2 Table 4 Figures 1,3, 4 Figure 2

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ROBERT KAIL

15

30

45

2

4

6

60

75

0

1

0 10

20

30

40

ADULTS' TIME (SEC)

50

0

i

ADULTS' TIME (SEC)

10

0

1

2

3

ADULTS' TIME (SEC)

4

0

2

4

6

8

10

12

ADULTS' TIME (SEC)

Figure 1. Fit of youth-adult mean response times to Equation 4, shown separately for 3-and 4-year-olds to 14-year-olds. (Each point represents the mean scores of youth and adult subjects from a condition in one of the studies listed in Table 1. Also shown is the linear function corresponding to predictions derived from Equation 4.)

adults' times for visual search decrease 6-fold and their times for solving geometry problems decrease 10-fold (Newell & Rosenbloom, 1981). The magnitude of change associated with children's practice is not well determined, but several investigators have shown that children's speeded performance improves with practice (Elliott, 1972; Pew & Rupp, 1971). Studies of practice provide another means by which to assess the accuracy of predictions from Equation 6. Specifically, some theorists claim that improvements associated with practice reflect more efficient performance, where efficiency often means that fewer steps are required for task performance (e.g., Anderson, 1983). Thus, if unpracticed performance involves the component times a, b, and c of Equation 1, practiced performance might be represented by d, the time to execute process D, the single process that is now responsible for task performance. Regardless of the specific mechanisms responsible for the effects of practice, implications for the present analyses are straightforward. Assuming that the impact of practice does not

differ qualitatively for youths and adults (i.e., Equations 1 and 2 apply), youths should still be slower than adults by the same value. nij. That is, if adults' RTs after practice reflect a single time d, then youths' RTs should equal m, d. Described in terms of the functions shown in Figure 1, in which youths' RT is expressed as a function of adults' RT, the expectation is that RTs before and after practice should both be well described by a straight line with a slope ofm, and intercept at the origin. The difference between unpracticed and practiced performance is that the latter points would be closer to the origin. These predictions were evaluated using practice data from Kail (1986a). In this study, 9-year-olds, 13-year-olds, and adults were tested on a mental rotation task for 16 days, receiving 240 trials daily. For the present analyses, RTs were used from the first and last days. Specifically, there were 24 mean RTs for each age group: 6 (orientations) X 2 (responses) X 2 (days[first, last]). Shown in Figure 4 are mean RTs for 9- and 13-year-olds as a function of adults' RTs in the same conditions. Also shown is

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Table 2 Fit of Youth-Adult RTs to Equation 4 All cases

RTs < 2 s

Age

(yr)

N

£2.

m,

N

R2,

3-4 5 6 7

54 89 158 173 366 267 285 173 167 43 51

.966 .950 .997 .967 .908 .957 .916 .996 .968 .981 .996

3.102 2.780 1.619 2.465 2.212 1.637 1.780 1.387 1.045 1.411 1.290

54 89 152 163 261 248 197 147 142 33 33

.966 .950 .927 .900 .813 .946 .942 .981 .975 .971 .997

8 9

10 11 12 13 14

m,

3.102 2.780 1.783 2.406 1.811 1.614 1.706 1.378 1.369 1.309 1.186

Note. RT = response time; N= number of conditions (i.e., the number of pairs of youth-adult RTs); m, = the slowing coefficient, estimated by the slope of the function relating youths' RTs to adults' RTs. * All /?2s are significant, p < .01.

the function with slope equal to m, and intercept = 0, where m, is derived independently from Equation 6 with b = 5.16 and c = .20811 (w9.5 = 1.72, w13.3 = 1.33). In the case of the 9-year-olds, the expected RTs account for 92.66% of the variance in youths' actual RTs. The expected values are quite accurate for practiced performance but slightly underestimate unpracticed performance. For 13-year-olds, the expected RTs account for 94.54% of the variance in youths' actual RTs, with no evidence of systematic mispredictions of those RTs.

Discussion

6. The problem here was that the procedures that subjects used to solve the analogical reasoning task apparently differed by age. In cases like this, there is no basis for predicting youth RTs as a function of adult RTs because the processes that make up RT are not the same for youths and adults. That is, youths' RTs are expected to be a multiple of adults' RTs only if the solution strategies represented in Equations 1 and 2 are the same for youths and adults. More generally, age differences in use of strategies represent certainly another independent factor responsible for age differences in performance on speeded tasks. For example, a number of different strategies can be used to solve addition problems (Siegler, 1987). Some strategies, such as retrieval, are rapid; others, such as counting aloud, are much slower. Age differences in processing speed will sometimes reflect use of more efficient strategies by older individuals. Occasionally, by virtue of greater experience with a task, the usual pattern of age differences will be reduced or eliminated because younger individuals have more task-appropriate knowledge and strategies (Chi, 1977). For example, children who are chess experts scan chessboards at a rate that does not differ significantly from that of adult novices (Roth, 1983). Cases like this make it clear that all age differences in processing speed cannot be explained solely in terms of age differences in some general factor. Instead, a

ALL RTs

o

Ul

The primary results of the analyses presented here were (a) during childhood and adolescence, youth RTs increase linearly as a function of adult RTs in corresponding conditions, and (b) the amount of increase—that is, the slope of the function (m,)—becomes smaller with age in a manner that is well described by an exponential function. One way to summarize these results succinctly is to insert Equation 6, which provides predictions concerning change in w, with age, into Equation 4:

l/l UJ Q_ O

RTs < 2 sec

be~")X.

(8)

As before, Y is predicted RT for youths, X is actual RT for adults, b = 5.16, and c = .20811. As age (0 approaches maturity, be~" approaches 0, so that predicted RTs approach X, adults' actual RTs. This finding is consistent with the view that age differences in processing speed are linked to some general factor (i.e., to one that is not specific to a particular task or class of tasks), and that this general factor changes exponentially with age. In the remainder of this article, I first discuss some limiting conditions on the claim that a general factor is responsible for age differences in processing speed. Then I suggest some possible candidates for the proposed general factor. Limiting Conditions Recall that in the initial analysis, findings from Kail (1988, Exp. 2) were not well described by values from Equations 4 and

LJ 0. O

8

10

12

14

16

18

20

AGE (YR)

Figure 2. Change in m,, the slowing coefficient, as a function of age. (The top panel depicts slowing coefficients derived from the entire data set; the bottom panel shows slowing coefficients derived from conditions in which adult response times [RTs ] s 2 s. Also shown are the best fitting exponential functions.)

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ROBERT KAIL

3 Kail (1986, Expt. 1)

Kail (1988, Expt. 2) All tasks

o

2

Q-

O

a

a

Kail (1988, Expt. 1)

n a

a a

D

Kail (1988, Expt. 2) 3 tasks

o

DD

2 -

a UJ Q.

O

a a

a D

1 -

10

12

14

16

18

AGE (YR)

20

10

12

14

16

18

20

AGE (YR)

Figure 3. Change in m,, the slowing coefficient, as a function of age. (The squares depict values determined from Equation 4. The exponential functions depict expected values derived from Equation 6 with 6=5.16 and c= .20811. The data are from Kail, 1986b, 1988.)

complete account of age differences in processing speed will include both general and domain-specific components.

Possible Mechanisms One explanation of this common rate of change is positive transfer between speeded processes (e.g., Stigler, Nusbaum, & Chalip, 1988). Skills used for particular tasks are said to generalize to other domains. For example, improved mental rotation skill with age might lead to faster memory search and faster visual search. Extensive positive transfer between numerous cognitive processes could result in common patterns of development for those processes, which would explain why a single value of m, at age /' characterizes youth-adult RTs and why m, changes regularly with age. The drawback to this explanation is that transfer between speeded tasks is typically specific: Positive transfer occurs only when tasks share a number of processes (e.g., Anderson, 1987). Considerable transfer from, for example, mental rotation to memory search is unlikely (Kail & Park, 1990). Given this relatively limited range of positive transfer between processes, transfer alone probably cannot account for a common rate of change with age. Another explanation concerns the quantity of processing resources available to execute speeded processes (Kail, 1986b, 1988). According to this explanation, increased processing

speed (decreased processing time) across tasks reflects an agerelated increase in the processing resources that can be allocated to the task. That is, processing resources may increase exponentially with age, and these increased resources yield faster performance on speeded tasks. There are at least two variations of this explanation (Case, 1985). One holds that the absolute quantity of resources increases with age, reflecting underlying maturational change. Another holds that the absolute quantity of resources is constant throughout development. However, with age, individuals are more likely to have acquired sufficient experience so that at least some components of a task can be executed automatically, that is, without drawing on processing resources. The result is a functional increase in the amount of resources available to processes that cannot yet be executed automatically. The drawback to these explanations is that a single common pool of resources is inconsistent with many studies of dual-task interference. If a single pool of resources is available, then performance on two tasks performed concurrently should be worse than performance on the tasks performed alone. The difference reflects the fact that concurrent task performance requires that a limited pool of resources be allocated between two tasks. However, concurrent task performance often is not reduced, which has led some theorists to propose multiple pools of resources (e.g., Wickens & Benel, 1982). For the multi-

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499

SPEED OF PROCESSING

o

O

o

9-YEAR-OLDS 1

2

ADULTS' TIME (SEC)

1

2

ADULTS' TIME (SEC)

Figure 4. Change in youths' response time (RT) as a function of adults' Rls, from Kail (1986a), separately for 9- and 13-year-olds. (The triangles denote performance on the first day of practice; the squares represent performance on the last day. Also shown are the functions far m9 5 =1.72 and m,3 3 = 1.33 [derived from Equation 6 with b ~ 5.16 and c = .20811] with the intercept = 0.)

pie resource view to explain the present results, either all of the processes known to conform to Equation 4 and 6 tap the same pool or the tasks tap distinct pools, but these develop at the same rate. A third explanation is derived from an analogy to computer hardware (Salthouse & Kail, 1983). If two computers have identical software but one machine has a slower cycle time (i.e., the time for the central processor to execute a single instruction), that machine will execute all processes more slowly by an amount that depends on the total number of instructions to be executed. The human analog to cycle time might be the time to scan the productions (i.e., condition-action instructions) in working memory, or it might refer to the time to execute the action side of a production (Klahr, 1989). In either case, a developmental decrease in the human cognitive cycle time would be associated with decreased time to complete cognitive operations. These candidates cannot be evaluated from the present analyses. Additional research is needed to (a) identify the general mechanism, (b) reveal why it changes nonlinearly with development, and (c) determine its interaction with domain-specific processes. What has been established here, however, is that age-related change in speeded performance is lawful and readily described quantitatively and apparently implicates a mechanism common to performance on a large and diverse assortment of speeded tasks.

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